Question

Which of hte following numbers are cubes of negative integers.
(i) -64 (ii) -1056 (iii) -2197 (iv) -2744 (v) -42875

Answer 1

(i)$-64=-(\underset{–}{2\times 2\times 2}\times \underset{–}{2\times 2\times 2})$

$\because$ All factors of 64 can be grouped in triplets of the equal factors completely.
$\therefore -64$ is a perfect cube of negative integrer

(ii) $-1056=\underset{–}{-(2\times 2\times 2)}\times 2\times 2\times 3\times 11$

$\because$ All the factors of 1056 can be grouped triplets of equal factors grouped completely
$\therefore -1058$ is not a perfect cube of negative integer.
(iii) $-2197=-\left(2197\right)=-\left(\underset{–}{13\times 13\times 13}\right)$

$\because$ All the factors of -2197 can be grouped in triplets of equal factors completely
$\therefore -2197$ is a perfect cube of negative integer.
$\left(iv\right)-2744=-\left(2744\right)=-(\underset{–}{2\times 2\times 2}\times \underset{–}{7\times 7\times 7})$

\because All the factors of - 2744 can be grouped in triplets of equal factors completely
$\therefore -2744$ is a perfect cube of negative integer
(v) $-42875=-\left(42875\right)=-(\underset{–}{5\times 5\times 5}\times \underset{–}{7\times 7\times 7})$

$\because$ All the factors of -42875 can be grouped in triplets of equal factors completely
$\therefore -42875$ is a perfect cube of negative integer.